Problem: What do the following two equations represent? $-5x+5y = 3$ $15x-15y = -9$
Solution: Putting the first equation in $y = mx + b$ form gives: $-5x+5y = 3$ $5y = 5x+3$ $y = 1x + \dfrac{3}{5}$ Putting the second equation in $y = mx + b$ form gives: $15x-15y = -9$ $-15y = -15x-9$ $y = 1x + \dfrac{3}{5}$ The above equations turn into the same equation, so they represent equal lines.